Modeling of directional solidification of multicrystalline silicon in a traveling magnetic field

Melt flow plays an important role in directional solidification of multicrystalline silicon influencing the temperature field and the crystallization interface as well as the transport of impurities. This work investigates the potential of a traveling magnetic field (TMF) for an active control of the melt flow. A system of 3D numerical models was developed and adapted based on open-source software for calculations of Lorentz force, melt flow, and related phenomena. Isothermal and non-isothermal model experiments with a square GaInSn melt were used to validate the numerical models by direct velocity measurements. Several new 3D flow structures of turbulent TMF flows were observed for different melt heights. Further numerical parameter studies carried out for silicon melts showed that already a weak TMF-induced Lorentz force can stir impurities near to the complete mixing limit. Simultaneously, the deformed temperature field leads to an increase of the deflection of crystallization interface, which may exhibit a distinct asymmetry. The numerical results of this work were implemented in a research-scale silicon crystallization furnace. Scaling laws for various phenomena were derived allowing a limited transfer of the results to the industrial scale

Lumped Parameter Model for Silicon Crystal Growth from Granulate Crucible

In the present paper, a lumped parameter model for the novel Silicon Granulate Crucible (SiGC) method is proposed, which is the basis for a future model-based control system for the process. The model is analytically deduced based on the hydromechanical, geometrical, and thermal conditions of the process. Experiments are conducted to identify unknown model parameters and to validate the model. The physical consistency of the model is verified using simulation studies and a prediction error of below 2% is reached. © 2020 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinhei

Numerical Simulation of Species Segregation and 2D Distribution in the Floating Zone Silicon Crystals

The distribution of dopants and impurities in silicon grown with the floating zone method determines the electrical resistivity and other important properties of the crystals. A crucial process that defines the transport of these species is the segregation at the crystallization interface. To investigate the influence of the melt flow on the effective segregation coefficient as well as on the global species transport and the resulting distribution in the grown crystal, we developed a new coupled numerical model. Our simulation results include the shape of phase boundaries, melt flow velocity and temperature, species distribution in the melt and, finally, the radial and axial distributions in the grown crystal. We concluded that the effective segregation coefficient is not constant during the growth process but rather increases for larger melt diameters due to less intensive melt mixing

Czochralski growth of tin crystals as a multi-physical model experiment

A new setup for Czochralski growth of model materials in air atmosphere has been developed. It includes various in-situ measurements to access the basic physical phenomena on a macroscopic level: heat transfer, electromagnetism, melt and gas flows, crystal stresses. A reference experiment with tin is performed and analyzed using simple analytical estimates as well as 2D numerical simulations with open source models. This study aims to improve the basic physical understanding of the Czochralski growth process and to provide a useful tool for education and research, both for non-specialists and scientists

Modeling of directional solidification of multicrystalline silicon in a traveling magnetic field

Melt flow plays an important role in directional solidification of multicrystalline silicon influencing the temperature field and the crystallization interface as well as the transport of impurities. This work investigates the potential of a traveling magnetic field (TMF) for an active control of the melt flow. A system of 3D numerical models was developed and adapted based on open-source software for calculations of Lorentz force, melt flow, and related phenomena. Isothermal and non-isothermal model experiments with a square GaInSn melt were used to validate the numerical models by direct velocity measurements. Several new 3D flow structures of turbulent TMF flows were observed for different melt heights. Further numerical parameter studies carried out for silicon melts showed that already a weak TMF-induced Lorentz force can stir impurities near to the complete mixing limit. Simultaneously, the deformed temperature field leads to an increase of the deflection of crystallization interface, which may exhibit a distinct asymmetry. The numerical results of this work were implemented in a research-scale silicon crystallization furnace. Scaling laws for various phenomena were derived allowing a limited transfer of the results to the industrial scale

Modeling of directional solidification of multicrystalline silicon in a traveling magnetic field

Melt flow plays an important role in directional solidification of multicrystalline silicon influencing the temperature field and the crystallization interface as well as the transport of impurities. This work investigates the potential of a traveling magnetic field (TMF) for an active control of the melt flow. A system of 3D numerical models was developed and adapted based on open-source software for calculations of Lorentz force, melt flow, and related phenomena. Isothermal and non-isothermal model experiments with a square GaInSn melt were used to validate the numerical models by direct velocity measurements. Several new 3D flow structures of turbulent TMF flows were observed for different melt heights. Further numerical parameter studies carried out for silicon melts showed that already a weak TMF-induced Lorentz force can stir impurities near to the complete mixing limit. Simultaneously, the deformed temperature field leads to an increase of the deflection of crystallization interface, which may exhibit a distinct asymmetry. The numerical results of this work were implemented in a research-scale silicon crystallization furnace. Scaling laws for various phenomena were derived allowing a limited transfer of the results to the industrial scale

Application of the Alexander–Haasen Model for Thermally Stimulated Dislocation Generation in FZ Silicon Crystals

Numerical simulations of the transient temperature field and dislocation density distribution for a recently published silicon crystal heating experiment were carried out. Low- and high-frequency modelling approaches for heat induction were introduced and shown to yield similar results. The calculated temperature field was in very good agreement with the experiment. To better explain the experimentally observed dislocation distribution, the Alexander–Haasen model was extended with a critical stress threshold below which no dislocation multiplication occurs. The results are compared with the experiment, and some remaining shortcomings in the model are discussed

Lumped Parameter Model for Silicon Crystal Growth from Granulate Crucible

In the present paper, a lumped parameter model for the novel Silicon Granulate Crucible (SiGC) method is proposed, which is the basis for a future model-based control system for the process. The model is analytically deduced based on the hydromechanical, geometrical, and thermal conditions of the process. Experiments are conducted to identify unknown model parameters and to validate the model. The physical consistency of the model is verified using simulation studies and a prediction error of below 2% is reached. © 2020 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinhei

Numerical Simulation of Species Segregation and 2D Distribution in the Floating Zone Silicon Crystals

The distribution of dopants and impurities in silicon grown with the floating zone method determines the electrical resistivity and other important properties of the crystals. A crucial process that defines the transport of these species is the segregation at the crystallization interface. To investigate the influence of the melt flow on the effective segregation coefficient as well as on the global species transport and the resulting distribution in the grown crystal, we developed a new coupled numerical model. Our simulation results include the shape of phase boundaries, melt flow velocity and temperature, species distribution in the melt and, finally, the radial and axial distributions in the grown crystal. We concluded that the effective segregation coefficient is not constant during the growth process but rather increases for larger melt diameters due to less intensive melt mixing